If Jacob receives by consuming ice-cream cone (X) and hamburger (Y) at Burger King is represented by the utility function U(X;Y) = XY. In addition, the per-unit prices of ice-cream cone and hamburger are $1 and $3 respectively. Jacob has an income of $24 to spend on the two goods.
Derive Jabob's budget constraint equation.
What is the slope of the budget line?
Derive the marginal utility of good X (MUX) using partial differentiation
Derive the marginal utility of good Y (MUY) using partial differentiation.
Using the equlibrium condition -MUX/MUY = -PX/PY to derive the quantity of each good consumed at the utility-maximizing equilibrium.
What is the utility level?
If income now doubles, while there is no change to the per-unit price of the two goods, derive the quantity of each good consumed as well as the utility level at the new equilibrium. What type of goods are X and Y?